SAT Solver Truth Table Construction Eliminates CNF Conversion Overhead
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Solution Overview
Problem
Existing SAT solvers face significant computational overhead and inefficiency in solving small-sized Boolean satisfiability problems due to the need for Conjunctive Normal Form (CNF) conversion, which introduces additional variables and clauses, and is not friendly for hardware implementation, leading to performance and capacity issues in hardware-based SAT solvers.
Innovation Solution
The approach involves constructing truth tables using Boolean vector interpretation to directly solve small-sized SAT problems, reducing the overhead of CNF conversion and improving performance by representing Boolean formulas as superpositions of bitwise unary and binary Boolean operators, and using iterative methods to assign values and infer variable values efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional SAT solvers use CNF conversion to solve Boolean satisfiability problems, then they can handle general SAT problems, but they introduce significant computational overhead and additional variables and clauses
Solution Approach 1:
The patent extracts and removes the CNF conversion step from the SAT solving process. By directly working with the original Boolean formula representation instead of converting to CNF, the method eliminates the computational overhead and additional variables/clauses that CNF conversion introduces, while still maintaining the ability to solve general SAT problems through direct interpretation and truth table analysis
Solution Approach 2:
Instead of the conventional approach of converting Boolean formulas to CNF form before solving, the patent inverts the process by directly interpreting and analyzing the original Boolean formula structure. This inversion allows the solver to work with the native representation, avoiding the overhead of conversion while preserving problem-solving capability through alternative methods such as truth table construction and direct satisfiability checking
2Reliability
If conventional SAT solvers convert Boolean formulas to CNF form, then they can solve SAT problems, but hardware implementation becomes inefficient and capacity is reduced
Solution Approach 1:
The patent substitutes the mechanical CNF conversion process with a direct interpretation and truth table analysis approach. In hardware implementations, this replacement eliminates the need for complex conversion circuits and enables more efficient direct evaluation of Boolean formulas, thereby improving both performance and capacity while maintaining solving correctness
Solution Approach 2:
The patent changes the fundamental parameter of representation from CNF form to direct Boolean formula interpretation. This parameter change allows hardware solvers to operate more efficiently by working with the original formula structure, reducing the capacity requirements and improving performance while maintaining the reliability of SAT problem solving through alternative evaluation methods
Data Source
AI summary
Techniques and systems for solving Boolean satisfiability (SAT) problems are described. Some embodiments solve SAT problems using efficient construction of truth tables. Some embodiments can improve performance of SAT solvers by using truth tables instead of incurring the overhead of Conjunctive Normal Form (CNF) conversion.